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A Random Walk Through Astrometry

A Random Walk Through Astrometry. Astrometry: The Second Oldest Profession. George H. Kaplan Astronomical Applications Department Astrometry Department U.S. Naval Observatory. Random Topics to be Covered. Astronomical reference frames Units Angles: Arcseconds

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A Random Walk Through Astrometry

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  1. A Random Walk Through Astrometry Astrometry: The Second Oldest Profession George H. Kaplan Astronomical Applications Department Astrometry Department U.S. Naval Observatory

  2. Random Topics to be Covered • Astronomical reference frames • Units • Angles: Arcseconds • Brightness: Magnitudes (and star density) • Moving from the optical into the infrared

  3. Astrometry: What is it? Why do it? • What: The science of measuring the positions and motions of celestial objects and interpreting the results • Why: • Many practical applications, involving navigation (broadly interpreted) and timekeeping • Sets the fundamental distance scale of the universe • Established the universality of gravitational law • Provides information on the evolution of the solar system and galaxy

  4. DoD Uses for Astrometric Data • Astro-inertial navigation systems ICBM guidance • Azimuth calibration • Deflection of the vertical determination • Satellite attitude control / sensor orientation • Ground-based satellite tracking, orbit determination • Near Earth object (NEO) detection • Standard celestial navigation • Determining astronomical time and Earth orientation for GPS

  5. These applications generally involve measuring something against a background of stars. . . . . . that is, motions of objects are measured within a celestial reference frame

  6. What is an Astronomical Reference Frame? An ensemble of coordinate values (and their rates of change) assigned to specific astronomical objects for a given epoch For example, the data in a star catalog This is completely analogous to the establishment of a geodetic reference system using an ensemble of Earth-fixed benchmarks whose coordinates are have been determined

  7. (2.37, +26.1) (–1.21, +22.8) (0.89, +18.4) (1.32, +5.9) (3.10, +1.7) (–2.05, –1.7) (1.52, –3.4)

  8. Types of Astronomical Reference Frames • Extragalactic Fiducial points are quasars or nuclei of galaxies • Constructed from radio  observations (VLBI) • No assumed angular motions — too far away • But …radio sources often variable • Galactic (Stellar) Fiducial points are stars • Lots of energy • Energy in  bands of practical use • But … stars move, sometimes in complex ways • Dynamical Fiducial points are planets or other orbiting bodies in the solar system (natural or artificial)

  9. Complications • Problem is over-determined: really only need two stars (3 coordinates) to define a reference frame • Therefore, for N stars in a catalog, ~N2/2 independent reference frame definitions — which will not, in general, be consistent due to errors in coordinate values • Not a bad problem as long as errors are random • If errors are a function of position on the sky, the reference frame is warped (systematic distortions) • Also problematic if errors are a function of magnitude or color

  10. (2.37, +26.1) (–1.21, +22.8) (0.89, +18.4) (1.32, +5.9) (3.10, +1.7) (–2.05, –1.7) (1.52, –3.4)

  11. (2.37, +26.1) (–1.21, +22.8) (0.89, +18.4) (3.10, +1.7) (–2.05, –1.7) (1.52, –3.4)

  12. Why star positions, and the reference frames they define, degrade with time 1950 1970 1980 Measured Path 1990 Actual Path

  13. You are here Stars are part of an inherently non-inertial system!

  14. Desirable Features ofAstronomical Reference Frames • Should define a local inertial reference system (no rotations) • Should be isotropic (no distortions) • Should be accurate • Should have a suitable density of fiducial points • Should have fiducial points detectable by relevant sensors (sufficient flux in sensor bandpass)

  15. Issues in Constructing Reference Frames • Stars part of galaxy, inherently a non-inertial system • Stars often part of binary or multiple systems • If resolved, orbital motions of components must be determined • If unresolved, photocenter may move or be f() • Parallax (distance) of stars must be determined • Quasars and AGNs have time-variable flux and structure • Aligning reference frames from different  regimes difficult — objects bright in one regime faint in the other

  16. Units! The Secret Code • Arcseconds • Magnitudes

  17. Angular Units: Arcseconds Application: Surface Nav LEO Geosync Distance: 1 R 500 km 35k km Angle 1 arcsec = 4.8 rad 31 m 2.4 m 170 m 0.1 arcsec = 0.48 rad 3.1 m 24 cm 17 m 1 mas = 4.8 nrad 3.1 cm 2.4 mm 17 cm 1 as = 4.8 prad 31 m 2.4 m 0.17 mm

  18. The Magnitude Scale • Goes back to Hipparcus (~150 BC), who divided naked eye stars into 6 categories of brightness 1 to 6, from brightest to faintest • Quantified in the 19th century: 5 magnitudes = factor of 100 in brightness  1 magnitude = factor of 2.512 in brightness • Now calibrated to absolute measures of energy received within a given wavelength band: U, V, B, R, I, J, H, K, L, u, v, b, y, etc. • Most common band V = mV = visual magnitude

  19. UBVRIJHKL Photometric Bands from The Astronomy and Astrophysics Encyclopedia, ed. S. P. Maran (1992)

  20. Scale of Visual Magnitude –4 Venus –1.5 Sirius 0 to 6 most naked-eye stars 5 Andromeda galaxy ~8 magnitude at which there is 1 star / degree2 9-10 faintest stars in binoculars 12 faintest stars in small (3-inch) telescope 12 brightest quasar (most are 15 and fainter) 14 Pluto 19.5 Palomar Sky Survey V limit (Palomar QV, 1980s) ~24 old photo plate limit with 200” telescope 29 current limit?

  21. Density of Astronomical Objects on the Sky • The volume of space enclosed by a radius d goes up as d3 • The apparent brightness L of an object at distance d falls off as d2 • The total number of objects brighter than apparent brightness L is proportional to L–3/2 • The total number of objects brighter than magnitude m is 3.98 times the number brighter than m–1

  22. Star Numbers vs. Magnitude Star Counts from Tycho-2 mv limit no. stars 5.0 1,658 3.44 6.0 5,713 3.18 7.0 18,183 2.98 8.0 54,192 2.85 9.0 154,656 2.70 10.0 417,769 2.59 11.0 1,083,253 1.99 12.0 2,158,589 Data courtesy Rob Olling

  23. Moving from the Optical into the Infrared (IR) • Why do it? • Issues

  24. Moving into the IR — Why? • Provides sensitivity to objects cooler than the surface of the Sun (~5800K). For example, peak radiation at: 0.7 m for 4000K 1 m for 2900K 1.5 m for 1900K 10 m for 300K • For astronomy, provides info on cool stars, brown dwarfs, “hot Jupiters”, star formation, interstellar dust, and highly redshifted galaxies • For DoD applications, provides sensitivity to rocket plumes, detonations of various kinds, and, at very long  (~10 m), to ordinary objects in equilibrium with ambient sunlight

  25. Moving into the IR — Why Not? • Detectors less well developed — can’t use CCDs (silicon) beyond above 1.1 m • Less resolution for given aperture size • Atmosphere opaque to IR except in certain windows Observations best from space • Bright background: • 1-2.5 m atmospheric emissivity, mainly due to OH • >2.5 m emissivity of everything else — telescope, optics

  26. Atmospheric Transmittance from Astrophysics: The Atmospheres of the Sun and Stars, L. H. Aller (1963)

  27. Catalog Issues • More stars! • Interstellar absorption less as  increases — see more stars • Galaxy contains more cool stars than hot • Can use optical data for stars in near IR, but … • Extrapolating IR magnitudes from visual very tricky • Completeness in visual to a certain magnitude in no way implies completeness in IR to similar magnitude • At magnitudes > 20, see many more galaxies very distant ones redshifted into the IR

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